Nonlinear mean reversion in the G7 stock markets

We utilize the nonlinear unit root tests proposed by Park and Shintani (2005) and find strong evidence of nonlinear mean reversion between a US stock index and the stock indices in France, Germany, Italy and the UK. We identified an inaction band where deviations of these international stock indices from the US stock index follow a unit root process. Outside the band, however, they exhibit strong mean reversion properties. We show that standard linear unit root tests are not able to detect nonlinear cointegration and will yield the erroneous conclusion that the stock indices are not cointegrated.